Find object location (x, y) in an image
What is a good model for this objective?


I will try to give another perspective: Solve it without machine learning model

Your problem is try to find the most overlapping point. If the image above is image that you used in your case, you can solve it directly by applying some computer vision algorithms.


Try to create some binary image based on the color of the dots. if you are not sure with the available colors on your image, you can list of pixel colors that not black and white uniquely at first. So if there are four colors you need to generate four different binary image. Create a simple condition or a complex one, for example:

if pixel[i,j]=red then
    pixel[i,j]=white
else
    pixel[i,j]=black

Get its location by searching "the white" over your image or use blob detection method (it'll be a little bit tricky if the actual image always have different axis scale). You can save it as a list of coordinate of each color.
What happen if you can't see the dot fully because it's overlapping with another dot? Find the pattern. In your image, dots appear with certain pattern. If you can find two consecutive dots horizontally and vertically, you can predict the position of all your dots.
Find the most overlapping position from your list. 


Pros


The result may more accurate than using machine learning model
Faster, you don't need to train it first


Cons


Finding dot's location in image with different axis will be difficult, but it's still solvable
It'll be difficult to predict the pattern if many dots are missing because overlapped by other dots